Let's assume that A has "x" rupees and B has "y" rupees.
First condition:
A says to B: "If you give me Rs. 100, my money will become 75% of the money left with you."
After B gives A Rs. 100, A will have (x + 100) rupees, and B will have (y - 100) rupees.
According to the condition, A's new amount (x + 100) will be 75% of B's remaining amount (y - 100).
So, the equation for the first condition is: (x + 100) = 0.75 * (y - 100) ---- (1)
Second condition:
B says to A: "If you give me Rs. 100, your money will become 40% of my money."
After A gives B Rs. 100, A will have (x - 100) rupees, and B will have (y + 100) rupees.
According to the condition, A's new amount (x - 100) will be 40% of B's new amount (y + 100).
So, the equation for the second condition is: (x - 100) = 0.40 * (y + 100) ---- (2)
Now, we have two equations:
(x + 100) = 0.75 * (y - 100)
(x - 100) = 0.40 * (y + 100)
Solving the system of equations:
From equation (1):
x + 100 = 0.75 * (y - 100) x + 100 = 0.75y - 75 x = 0.75y - 75 - 100 x = 0.75y - 175 ---- (3)
From equation (2):
x - 100 = 0.40 * (y + 100) x - 100 = 0.40y + 40 x = 0.40y + 40 + 100 x = 0.40y + 140 ---- (4)
Now, equate the expressions for x from equations (3) and (4): 0.75y - 175 = 0.40y + 140
Simplifying this: 0.75y - 0.40y = 140 + 175 0.35y = 315 y = 315 / 0.35 y = 900
Now that we have y = 900, substitute this value into equation (4) to find x: x = 0.40 * 900 + 140 x = 360 + 140 x = 500
Final Answer:
A originally had Rs. 500, and B originally had Rs. 900.
